Such a high-pressure discharge lamp is disclosed, for example, in WO 98/18297. This laid-open patent application describes a high-pressure discharge lamp having an auxiliary starting electrode and a pulse starting device, arranged in the lamp base, for starting the gas discharge in the discharge vessel of the high-pressure discharge lamp. The pulse starting device and the operating circuit for the high-pressure discharge lamp are electrically isolated from one another by means of a transformer. Both the pulse starting device and the operating circuit are connected in each case for their voltage supply to a secondary winding of the transformer, whose primary windings are designed as a constituent of a push-pull inverter. The pulse starting device is shut down after successful starting of the gas discharge by means of a semiconductor switch.